# Preliminary Schedule of the Conference

## Tuesday, May 2

10:00 - 10:30 |
Registration & Welcome coffee |

10:30 - 10:45 |
Opening remarks |

10:45 - 11:35 |
Bauer |

11:45 - 12:35 |
Michael Kerber: Novel computational perspectives of Persistence |

12:35 - 14:10 |
Lunch break |

14:10 - 15:00 |
Giusti |

15:10 - 16:00 |
Herlihy |

16:00 - 16:30 |
Tea and cake |

16:30 - 17:20 |
Rajsbaum |

afterwards |
Reception |

## Wednesday, May 3

9:10 - 10:00 |
Chen |

10:00 - 10:30 |
Group photo and coffee break |

10:30 - 11:20 |
Yasu Hiraoka: Limit theorem for persistence diagrams and related topics |

11:30 - 12:20 |
Reitzner |

12:20 - 14:10 |
Lunch break |

14:10 - 15:00 |
Brodzki |

15:10 - 16:00 |
Weinberger |

16:00 - 16:30 |
Tea and cake |

16:30 - 17:30 |
Poster session |

## Thursday, May 4

9:10 - 10:00 |
Bianconi |

10:00 - 10:30 |
Coffee break |

10:30 - 11:20 |
Dmitri Krioukov: Exponential Random Simplicial Complexes |

11:30 - 12:20 |
Meshulam |

12:20 - |
Lunch break, free time (excursion?) |

## Friday, May 5

9:10 - 10:00 |
Fajstrup |

10:00 - 10:30 |
Coffee break |

10:30 - 11:20 |
Jérémy Dubut: Natural homology: computability and Eilenberg-Steenrod axioms |

11:30 - 12:20 |
Krzysztof Ziemianski: Directed paths on cubical complexes |

12:20 - 14:10 |
Lunch break |

14:10 - 15:00 |
Peter Bubenik: Stabilizing the unstable output of persistent homology computations |

15:10 - 16:00 |
Turner |

16:00 - 16:30 |
Tea and cake |

16:30 - 17:30 |
Software demonstrations and discussions |

## Saturday, May 6

9:10 - 10:00 |
Fasy |

10:00 - 10:30 |
Coffee break |

10:30 - 11:20 |
José Perea: Topological time series analysis and learning |

11:30 - 12:20 |
Hubert Wagner: Topological Analysis in Information Spaces |

12:20 |
Farewell |

# Abstracts

## Peter Bubenik: Stabilizing the unstable output of persistent homology computations

Certain items of persistent homology computations are of particular interest to practitioners but are unfortunately unstable. For a notorious example, consider the generating cycle of a particular point in the persistence diagram. I will present a general framework for providing stable versions of such calculations. This is joint work with Paul Bendich and Alexander Wagner.

## Yasu Hiraoka: Limit theorem for persistence diagrams and related topics

In this talk, I will present a recent result about convergence of persistence diagrams on stationary point processes in R^{N}. Several limit theorems such as strong laws of large numbers and central limit theorems for random cubical homology are also shown. If I have time, recent progress on higher dimensional generalization of Frieze zeta function theorem is also presented.

## Michael Kerber: Novel computational perspectives of Persistence

The computational pipeline of topological data analysis consists of three major steps:

(1) Deriving a multi-scale representation of the underlying data set

(2) Computing topological invariants of that representation

(3) Interpreting the outcome of (2) to draw conclusions about the data

In my talk, I will present new results in all three steps. In particular,

@(1) an approximation scheme for Rips and Cech complexes in high dimensions,

@(2) an algorithm to compute persistence diagrams of sequences of general simplicial maps,

@(3) an efficient implementation for computing Bottleneck and Wasserstein distances of peristence diagrams.

These results are joint work with Aruni Choudhary, Dmitriy Morozov, Arnur Nigmetov, Sharath Raghvendra and Hannah Schreiber.

## Hubert Wagner: Topological Analysis in Information Spaces

Understanding high dimensional data remains a challenging problem. Topological Data Analysis (TDA) promises to simplify, characterize and compare such data. However, standard TDA focuses on Euclidean spaces, while many types of high-dimensional data naturally live in non-Euclidean ones. Spaces derived from text, speech, image, … data are best characterized by non-metric dissimilarities, many of which are inspired by information-theoretical concepts. Such spaces will be called information spaces.

I will present the theoretical foundations of topological analysis in information spaces. First, intuition behind basic computational topology methods is given. Then, various dissimilarity measures are defined along with information theoretical and geometric interpretation. Finally, I will show how the framework of TDA can be extended to information spaces. In particular, I will explain to what extent existing software packages can be adapted to this new setting.

This is joint work with Herbert Edelsbrunner and Ziga Virk.